Online Active Regression
This work addresses efficient label acquisition for regression in online settings, which is incremental as it extends existing active regression methods to an online framework.
The paper tackles the problem of online active regression, where a learner receives data points sequentially and must decide which labels to query to maintain an accurate linear regression model under a small budget, achieving a (1+ε)-approximate solution with only Õ(ε^{-1} d log(nκ)) label queries.
Active regression considers a linear regression problem where the learner receives a large number of data points but can only observe a small number of labels. Since online algorithms can deal with incremental training data and take advantage of low computational cost, we consider an online extension of the active regression problem: the learner receives data points one by one and immediately decides whether it should collect the corresponding labels. The goal is to efficiently maintain the regression of received data points with a small budget of label queries. We propose novel algorithms for this problem under $\ell_p$ loss where $p\in[1,2]$. To achieve a $(1+ε)$-approximate solution, our proposed algorithms only require $\tilde{\mathcal{O}}(ε^{-1} d \log(nκ))$ queries of labels, where $n$ is the number of data points and $κ$ is a quantity, called the condition number, of the data points. The numerical results verify our theoretical results and show that our methods have comparable performance with offline active regression algorithms.